gwenspooner85

Let x be the cost of a brownie and y the cost of a cookie. The amount of money Melvin spends is 4x+3y. The amount of money Lily spends is 2x+16y, which is double of 4x+3y(the amount of money Melvin spent). We then form an equation.

2(4x+3y)=2x+16y

8x+6y=2x+16y

6x=10y

x=5/3y

Therefore a brownie is 5/3 times as expensive as a cookie.

We write 3x+4y=-14 in slope intercept form.

3x+4y=-14

4y=-3x-14

y=-3/4x-14/4

The slope of the perpendicular line must be 4/3 because the two slopes must multiply to -1. 

We plug in the slope into y=mx+b to get y=4/3x+b. Then we plug in the given point to determine b, the y-intercept.

7=4/3(-5)+b

7=-20/3+b

b=7+20/3

b=41/3

Therefore the equation of the perpendicular line is y=4/3x+41/3.

Most Guests here are "cheating" on their AoPS homework as well. How would we know if you aren't either, hm?

1.

 \(2x - 5 \le -x +12\\ =3x\le17\\ =x\le\frac{17}{3}\\ \boxed{x\in(-\infty,\frac{17}{3}]}\)

2.

 \(-4(x+4)>x+7\\ -4x-16>x+7\\ -5x>23\\ 5x<-23\\ x<-\frac{23}{5}\\\ \boxed{x\in(-\infty, -\frac{23}{5})} \)

To find the x interept, plug in the value 0 for y in both equations.

y=1/3x+7

0=1/3x+7

1/3x=-7

x=-21

y=2x+5

0=2x+5

2x=-5

x=-5/2

Add them together. -21+(-5/2)=-23.5.

The even digits are 0, 2, 4, 6, 8.

For the leftmost digit, the first digit there are 4 choices(because 0 can't be the first number). For the second number, there are 10 choices(it can be both odd or even). For the third number, there are also 10 choices. For the fourth number, there are also 10 choices. Finally, the rightmost digit, has 5 choices(all the possible even digits: 0, 2, 4, 6, 8). 

So the total number of 5 digit numbers are: 4 * 10^3*5= 20*10^3=20000.

I'm not that good with counting so please tell me if this is correct.

Complete the square.

\(4x^2+5x+2\\ =4(x^2+\frac{5}{4}+\frac{1}{2})\\ =\boxed{4(x+\frac{5}{8})^2+\frac{7}{16}}\)

We plug the values into the quadratic equation to get the solutions \(\frac{11\pm\sqrt{41}}{10}\). I think you can do the rest from there.

To find the y-intercept, we plug 0 into the given equation for x.

3x-7y=21

3(0)-7y=21

-7y=21

y=-3

The y intercept is (0, -3).

To find the x-intercept, we plug 0 into the given equation for y.

3x-7y=21

3x-7(0)=21

3x=21

x=7

The x-intercept is (7, 0).

Plugging these values into the distance formula, the answer is \(\sqrt{58}\).

A horizontal line is the in the form of y=___. Then the line passing through (-5, 8) must be y=8. A vertical line is in the form of x=___. The the line passing through (4, -1) must be x=4. The point of intersection is therefore (4, 8).